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Re: A Paradox of Equality?

Newsgroups sci.logic
Date 2023-06-03 14:12 -0700
References (6 earlier) <bee217b6-b2b4-4e07-9285-457e803b94e3n@googlegroups.com> <u5g6hg$r4vl$1@solani.org> <d4872593-9a25-4ab8-8c94-1d31d328586cn@googlegroups.com> <0a3c1c44-1dfb-4c95-8135-de6b33984451n@googlegroups.com> <b20fab3e-3256-4fb5-87da-459884d9f2e3n@googlegroups.com>
Message-ID <1e7c01de-eb76-4c7b-89a1-d7564b71fbbdn@googlegroups.com> (permalink)
Subject Re: A Paradox of Equality?
From Mild Shock <bursejan@gmail.com>

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The proper de Morgan rules are interesting for 
mathematics and lattice theory, since one can 
find lattices that satisfy the de Morgan rules, 

including involution, but do not satisfy these 
rules that are part of "material implication". Namely:

quasi-boolean algebras
¬x ∨ x = 1 (law of the excluded middle), and
¬x ∧ x = 0 (law of noncontradiction)
https://en.wikipedia.org/wiki/De_Morgan_algebra

Which is quite interesting, since it has nevertheless
involution aka double negation elimination. But in
the setting of minimal logic, double negation elimination

implies both (law of the excluded middle) and
(law of noncontradiction). In minimal logic we can
also add either, (law of the excluded middle) or

(law of noncontradiction), whereas a quasi-boolean 
algebra collapses into a boolean algebra, if one of
the two is added.

Mild Shock schrieb am Samstag, 3. Juni 2023 um 22:56:34 UTC+2:
> The rules you implemented are even not part 
> of the square of opposition, nor part of de Morgan, 
> you implemented some replacement rules, the 
> 
> balance of these rules is that they add two negation 
> signs, thats why they are clumsy: 
> 
> /* Replacement Rules */
> EXIST(x):A(x) ~~> ~ALL(x):~A(x)
> ALL(x):A(x) ~~> ~EXIST(x):~A(x) 
> 
> The square of opposition has these 4 rules, 
> the balance of these rules are that they remove 
> two negations, or keep the number of negations the same: 
> 
> ~EXIST(x):~A(x) ~~> ALL(x):A(x) 
> ~ALL(x):~A(x) ~~> EXIST(x):A(x)
> ~EXIST(x):A(x) ~~> ALL(x):~A(x)
> ~ALL(x):A(x) ~~> EXIST(x):~A(x)
> https://en.wikipedia.org/wiki/Square_of_opposition 
> 
> Two of them are de Morgan. The de Morgan has these 
> 4 rules. The balance of these rules is that they 
> always keep the number of negations the same: 
> 
> ALL(x):~A(x) ~~> ~EXIST(x):A(x) 
> EXIST(x):~A(x) ~~> ~ALL(x):A(x)
> ~EXIST(x):A(x) ~~> ALL(x):~A(x)
> ~ALL(x):A(x) ~~> EXIST(x):~A(x)
> https://en.wikipedia.org/wiki/De_Morgan%27s_laws 
> 
> So you picked the worst inference rules, those 
> that add negation signs. Whereas for classical 
> logic there exist inference rules that remove 
> 
> negation signs or keep the number of negation 
> signs constant. Well Shit Happens!
> Mild Shock schrieb am Samstag, 3. Juni 2023 um 22:49:06 UTC+2: 
> > Its pretty obvious that they are clumsy nonsense. 
> > For example you implement only two rules: 
> > 
> > EXIST(x):A(x) ~~> ~ALL(x):~A(x) 
> > ALL(x):A(x) ~~~> ~EXIST(x):~A(x) 
> > 
> > But the Greeks where already discussing the 
> > square of opposition. Which hat 4 differnent 
> > 
> > https://en.wikipedia.org/wiki/Square_of_opposition 
> > 
> > formulas to start with and not only two. 
> > Notice something dumbo? So it wouldn't 
> > 
> > cost you much to allow the end user to 
> > additional perform the following operations: 
> > 
> > a) If the end user clicks on a negation sign ~ 
> > in front of an EXIST, this rule fires: 
> > 
> > ~EXIST(x):A(x) ~~> ALL(x):~A(x) 
> > 
> > b) If the end user clicks on a negation sign ~ 
> > in front of an ALL, this rule fires: 
> > 
> > ~ALL(x):A(x) ~~> EXIST(x):~A(x) 
> > 
> > Hope this Helps! 
> > 
> > Dan Christensen schrieb am Samstag, 3. Juni 2023 um 22:27:57 UTC+2: 
> > > > They are clumsy nonsense.

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A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 10:33 -0700
  Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-03 11:02 -0700
    Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 11:17 -0700
      Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-03 11:47 -0700
        Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:57 -0700
        Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 12:37 -0700
  Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:13 -0700
    Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:20 -0700
      Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:42 -0700
        Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 12:14 -0700
      Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 11:56 -0700
        Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 11:58 -0700
          Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 12:08 -0700
            Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 12:25 -0700
    Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 11:26 -0700
      Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 21:12 +0200
        Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 21:20 +0200
        Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 12:27 -0700
          Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 21:41 +0200
          Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 21:41 +0200
            Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 13:02 -0700
              Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-03 22:07 +0200
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 13:27 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 13:49 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 13:56 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 14:12 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-03 14:24 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-03 19:24 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 06:46 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 06:47 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 06:51 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 09:33 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 12:22 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 13:48 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 14:38 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 15:29 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-04 17:20 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 18:23 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 01:31 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 02:55 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 08:22 -0700
                Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-05 19:47 +0200
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 11:59 -0700
                Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-05 21:49 +0200
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 13:39 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 12:32 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 12:39 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 13:03 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 13:09 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 13:14 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 14:34 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:04 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:14 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:26 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 16:33 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 14:22 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:06 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 17:13 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 17:26 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 17:36 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 17:47 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 17:54 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 18:00 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 18:02 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 18:05 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 18:35 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 22:38 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 22:47 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-05 22:58 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-06 07:35 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-06 09:11 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-06 10:08 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-08 01:25 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 08:09 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-08 11:09 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-08 11:35 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-08 11:36 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-09 12:51 -0700
                Re: A Paradox of Equality? Mild Shock <bursejan@gmail.com> - 2023-06-09 13:12 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 18:17 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 18:44 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 14:09 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 14:32 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 17:42 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 18:32 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 19:04 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 19:15 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-05 20:39 -0700
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 08:43 -0700
                Re: A Paradox of Equality? Mild Shock <janburse@fastmail.fm> - 2023-06-04 17:55 +0200
                Re: A Paradox of Equality? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-04 09:40 -0700
                Re: A Paradox of Equality? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-04 10:42 -0700

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